When the hole in the center of a LP is off-center, the record wobbles in a horizontal plane. As long as the cartridge can track this "oval", does the sound suffer? I know a warped record will deflect the cartridge vertically, but it seems universally accepted that this DOES NOT affect sound. Same too for the horizontal bop? \:D/

Since the platter speed is fixed. An off center pressed record will have a relative speed that is faster on one half of a turn and slower on the other.
Speed equals pitch so played notes will sound sharp on one half and flat on the other.

Wether it bothers you is another question, as some people are very sensitive to pitch variations other seem not to notice it and just enjoy the music.

Me personally, I can't stand it, especially on piano notes...

The variations in speed are much smaller with warped record, but still, they can be audible...

wojo: Not only that, but there also is some speed variation due to so-called "scrubbing". I.e., on the majority of tonearms designs the axis for the vertical arm motion is not lowered onto record height, so that the actual effective length varies a tiny bit (or respectively more than necessary) with the arm angle (and with it also the alignment geometry). And the tracking force of course also varies a tiny bit with the arm angle - how exactly also depends on the particular design, though (mainly on whether its statically or dynamically balanced and how the counterweight is shaped and attached...).

Well, and regarding excentricity, you can pretty simply calculate the effect, as the speed deviation is directly proportional to the radius deviation. Typically one will tend to apply it to a playback radius of 100 mm, as that makes it easy to calculate and represents roundabout the middle of the LP playback area. So at 100 mm an excentricity of 0.2 mm would already mean a peak wow of +/- 0.2 % (or an RMS wow of that times 0.5^0.5 = ca. +/- 0.141 %). And due to the radius dependence with a playback radius range of ca. 60 to 145 mm one can of course also conclude, that the effect has to be almost 2.42 times as bad near the end of the record than at the beginning.

Warps are extremely low frequency signals, as far as the phono cartridge is concerned.
Watch your speaker's woofer as the stylus rides over a warp.
The woofer makes very large excursions in and out.
These low frequency signals can damage your woofers and the signal mixes with the musical signals to cause intermodulation distortion.
The amplifier can also be driven into clipping due to the amount of power needed to move the woofer so much at such a low frequency.

A low filter on your amp or preamp can reduce the effect, but sometimes won't eliminate it.

I'm surprised no one has mentioned channel imbalance. With the stylus moving back-and-forth horizontally, it slams into the groove walls with excess force, creating an imbalanced stereo signal. This can cause excess wear in the groove walls as well.

Warps are like riding a roller coaster, pulling more g-force in the dips (more amplitude in the signal...and again more wear), and less in the peaks (less detail as it rides lighter in the groove over the crest).

Perhaps 'slamming into' is a bit dramatic, so maybe 'riding up' on the groove walls is more palatable. Of course this is just centrifugal force, similar to riding in a car down a FLAT (no embankment) curvy road, where you slide in the seat back-and-forth around every curve - pressing against either the car door or the center console. The stylus will alternate riding up on the groove walls as it moves back-and-forth with an off-center record.

The February 1959 issue of Popular Mechanics has an article titled, "Hi-Fi Buyer's Guide: Tone Arms", which mentions this concept, and warps as well.

"Vertical motion of the record surface, due to warp, works against the arm's inertia to send tracking forces skyrocketing. Back and forth lateral motions of the arm due to record eccentricity produce destructive side forces with a high-inertia arm."p.215

Regarding viscous damping of tone arms, "On warped or off-center records, it offers the same drawbacks as high-intertia arms."p.216

Clearly, heavier tonearms create more of an issue with warped or off-center records.